Melt 2 Tbl of butter in a 12 inch, non-stick frying pan. Add the onion rings. Reduce the heat to medium-low. Saute the onions until they are golden-brown. From time to time, stir the onions.
Remove the excess moisture from the beef chunks with paper towels. Heat up a large Dutch oven over a medium flame. In 1 Tbl of oil and 1 Tbl of butter, brown the chunks, on all sides. Remove the beef from the pan. De-grease the pan.
When the onions are golden, add flour and saute for 2 minutes. Throw the onion/four mixture into the Dutch oven. De-glaze the Dutch oven with red wine. Whisk to combine. Deglaze the 12 inch frying pan with beef stock. Pour the deglazed contents of the frying pan into the Dutch oven. Completely break down the roux down with more whisking. Return the beef chunks to the pan. Add the garlic, cayenne pepper, and salt and pepper to taste. Bring the liquids in the pan to a rolling boil, cover the pan with a tightly fitting lid and cut the heat to a slow simmer. Braise for 1 1/2 hours (or until the beef is tender). Allow the pan to rest for 10 minutes.
Grate the cheese. Slice the bread thickly and toast it. Preheat the broiler. Place a portion of the beef and sauce into a small, broiler-proof dish. Repeat with 3 more such dishes until no beef and sauce remain. Arrange a slice of the bread and sprinkle grated Gruyere cheese over the bread for each dish. Broil until the cheese bubbles and becomes golden-brown. Serve immediately.